Recent advances in thin film technology have made it increasingly important to be able to accurately measure the characteristics of thin films. The thin film properties of interest include:
Thickness, d PA1 Index of Refraction, n PA1 Extinction Coefficient, k PA1 Energy Bandgap, E.sub.g PA1 Interface Roughness, .sigma. PA1 (a) is equally efficient at all wavelengths, thereby increasing the accuracy of the measurements; PA1 (b) comprises as few components as possible, thereby minimizing spurious loss of light and reducing the opportunity for misalignment; and PA1 (c) can provide for an adjustable range of angles of incidence of light upon the sample being studied.
The index of refraction n and the extinction coefficient k depend on the energy E of the photons involved; i.e., n=n(E) and k=k(E). The index of refraction n(E) describes how light is diffracted by a material. In similar materials, n(E) scales with the density of the material. The extinction coefficient, k(E), relates to the absorption of light. A material with a large extinction coefficient absorbs more light than a material with a small extinction coefficient. Transparent materials have an extinction coefficient of zero in the visible range of light. The energy bandgap, E.sub.g, represents the minimum photon energy needed for a direct electronic transition from the valence to the conduction band; i.e., for E&lt;E.sub.g, absorption of light due to direct electronic transitions is zero.
In general, determination of the above quantities is a non-trivial problem. The n(E) and k(E) spectra of a film cannot be measured directly, but must be deduced from optical measurements. U.S. Pat. No. 4,905,170 by Forouhi and Bloomer discloses a method for determining these spectra from the reflectance spectrum of the film. Their method involves shining light onto the film and observing how much light is reflected back. The reflectance spectrum, R(E), is defined as the ratio of the reflected intensity to the incident intensity of light. R(E) depends on the angle of incidence .theta. of the light upon the film, as well as the film thickness d, the indices of refraction and extinction coefficients n.sub.f (E) and k.sub.f (E) of the film, n.sub.s (E) and k.sub.s (E) of the substrate, the band gap energy of the film E.sub.g, and the interface roughness .sigma..sub.1 and .sigma..sub.2 of both the top and the bottom of the film. To characterize any film, it is necessary to de-convolute the optical measurement R(E) into its intrinsic components d, n.sub.f (E), k.sub.f (E), n.sub.s (E), k.sub.s (E),E.sub.g, .sigma..sub.1 and .sigma..sub.2.
The above patent by Forouhi and Bloomer incorporates a formulation for the optical constants n(E) and k(E), along with a parameterized model for interface roughness, into the Fresnel coefficients associated with films on a substrate (found in standard texts) to generate an algorithm that describes the theoretical reflectance; i.e., EQU R.sub.theory =R.sub.theory (E, .theta., d, n.sub.f (E), k.sub.f (E), n.sub.s (E), k.sub.s (E), E.sub.g, .sigma..sub.1, .sigma..sub.2)
By comparing the resultant equation for theoretical reflectance with the actual measurement of broad-band reflectance, the required parameters for thin film characterization d, n.sub.f (E), k.sub.f (E), E.sub.g, and .sigma..sub.1 and .sigma..sub.2 can be determined.
To measure the reflectance R(E), light must be generated by a source and reflected by the sample into a spectrophotometer. Typically, lenses are used to build an optical relay that directs the light from the source to the sample, and from the sample to the spectrophotometer. (An optical relay is a device that produces an image at one point from a source at another point.) The many different materials used in the fabrication of coatings have characteristic reflectance peaks that range from the ultraviolet to the infrared. Therefore, the reflectance spectrum of the sample should be measured for wavelengths in the range from about 190 nm to 1000 nm. Unfortunately, over this wide range of wavelengths, simple lenses exhibit a significant amount of chromatic aberration: the focal length typically changes by about 20% from one end of the spectrum to the other. Therefore any optical relay using lenses will be more efficient at some wavelengths than at others. This means that the measured spectrum will be distorted.
U.S. Pat. No. 4,784,487 by Hopkins and Willis describes an optical relay for spectrophotometric measurements that partially compensates for this chromatic aberration by a skillful use of apertures. There are two difficulties with this relay in the present context. First, the relay was developed for transmittance rather than reflectance measurements. Even if the relay is adapted for reflectance measurements, however, it will still be extremely sensitive to small misalignments. This is because when the light beam is reflected by the sample and focused onto the entrance slit of the spectrophotometer, the pencil of light entering the spectrophotometer is not chromatically homogeneous, but is, for example, red in the center and blue toward the edges. If a misalignment occurs, the input beam is no longer exactly centered on the entrance slit, and not only does the intensity of measured light decrease, but the relative ratio of blue to red changes. This is disastrous to the above method of characterizing thin films, since the method relies on measuring all parts of the reflected spectrum equally well. Small and unavoidable misalignments therefore lead to incorrect characterizations of the thin film.
Furthermore, it is desirable for an optical relay used for thin film characterization to have as few components as possible to minimize the opportunities for misalignment and to minimize the light lost by reflections from each surface. It is also desirable to use an optical relay that allows light to strike the sample with a range of angles of incidence, this range being chosen to simplify the interpretation of the reflectance R(E) in terms of thin film properties.